Alphabeta Math

The Inverse and Implicit Function Theorems

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The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

  • Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
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✓ 3 results · all verified · 0 also independently AI-judged
Every result on this page is machine-checked by a proof checker and read in full and owner-audited; the judge is an additional, independent cross-model AI review of the proofs. The 3 not AI-judged were verified by owner audit (typically over a confirmed judge false positive), not failures.
1 · Prerequisites
Abstract Algebra
Linear Algebra
Real Analysis
Set Theory
Topology
2 · Logical flowchart

3 · Items

Definition

Continuously differentiable maps, local inverses, and local diffeomorphisms

Definition

Invertible Euclidean linear maps

Lemma

Newton maps are uniform contractions near a point with invertible derivative

Theorem

The Euclidean inverse function theorem

Theorem

The Euclidean implicit function theorem with derivative formula

Sources